<p>In this paper, we introduce the convolution of the imaginary Lebedev-Skalskaya transform. The Parseval equality and the factorization equality for the imaginary Lebedev-Skalskaya convolution are established. Basing on the structure of this convolution, a class of integro-differential operators of Ritt’s type associated with the imaginary Lebedev-Skalskaya convolution is considered. As applications, some classes of related integro-differential equations are also considered.</p>